MATHEMATICS HIGH SCHOOL

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x3 + 8x2 = 450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.4 inches
5 inches
9 inches
10 inches

Answers

Answer 1
Answer:

The length of the side of the original cube in the given scenario is 5 inches.

A cube is a three-dimensional figure with equal sides.

Given that

The length of the edge of a cube = x

Also, one of the sides is increased by 4 inches, and another side is doubled,

so, now the new dimensions are x, x+4, 2x, and the shape is a rectangular prism.

The area of the rectangular prism = 450 sq. inches

base × height × length = 450 sq. inches

x × (x + 4) × 2x = 450

2x³ + 8x² = 450

2x³ + 8x² - 450 = 0

x³ + 4x² - 225 = 0

Substitute x=5  to see that it is a root of the equation,

5³ + 4(5)² - 225 = 125 + 100 - 225 = 0

So, x - 5 is a factor of the equation,

Now,

x³ + 4x² - 225 = (x−5)(x² + 9x + 45) = 0

The roots of the quadratic equation are imaginary as

D = 9² - 4 × 1 × 45 = 81 - 180 = -99

The discriminant is negative, therefore, the roots are not real.

So, the length of the side of the original cube is 5 inches.

Learn more about Cubes here:

brainly.com/question/29420559

#SPJ4
Answer 2
Answer: the answer  i got is 5 inches  im glad to help

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Answers

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